I shut down my computer because I was going to sleep. The next morning I tried to turn on my computer but the power button won't even turn on. I've tried to hold the power button down for 30 seconds and that didn't work.

Have you tried to boot the laptop with only the charger plugged in? If you have, you couldn't see any light to blink and everything remained silent, is that true?
If the warranty of your laptop has expired, I suggest you to take out the hard drive and try to connect it to another computer through SATA-USB cable. If your hard drive spins up on a different computer and it is recognized there, but cannot power up on your laptop, then the problem is hiding probably in the power supply unit on your motherboard.
While on another PC, I suggest you to make a full backup of your files just in case of a need for a motherboard replacement.
You could also bring your laptop to a technician to make a test of the power connector and/or the power jack center because they might have got damaged.